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Many real world problems can be mapped onto graphs and solved with well-established efficient algorithms studied in graph theory. One such problem is to find large sets of points satisfying some mutual relationship. This problem can be transformed to the problem of finding all cliques of an undirected graph by mapping each point onto a vertex of the graph and connecting any two vertices by an edge whose corresponding points satisfy our desired relationship. Clique detection has been widely studied and there exist efficient algorithms. In this paper we study a related problem, where all points have a set of binary attributes, each of which is either 0 or 1. This is only a small limitation, since all discrete properties can be mapped onto binary attributes. In our case, we want to find large sets of points not only satisfying some mutual relationship; but, in addition, all points of a set also need to have at least one common attribute with value 1. The problem we described can be mapped onto a set of induced subgraphs, where each subgraph represents a single attribute. For attribute $i$, its associated subgraph contains those vertices corresponding to the points with attribute $i$ set to 1. We introduce the notion of a maximal clique of a family, $\mathcal{G}$, of induced subgraphs of an undirected graph, and show that determining all maximal cliques of $\mathcal{G}$ solves our problem. Furthermore, we present an efficient algorithm to compute all maximal cliques of $\mathcal{G}$. The algorithm we propose is an extension of the widely used Bron-Kerbosch algorithm.
In this paper we describe a new algorithm for multiple semi-flexible superpositioning of drug-sized molecules. The algorithm identifies structural similarities of two or more molecules. When comparing a set of molecules on the basis of their three-dimensional structures, one is faced with two main problems. (1) Molecular structures are not fixed but flexible, i.e., a molecule adopts different forms. To address this problem, we consider a set of conformers per molecule. As conformers we use representatives of conformational ensembles, generated by the program ZIBMol. (2) The degree of similarity may vary considerably among the molecules. This problem is addressed by searching for similar substructures present in arbitrary subsets of the given set of molecules. The algorithm requires to preselect a reference molecule. All molecules are compared to this reference molecule. For this pairwise comparison we use a two-step approach. Clique detection on the correspondence graph of the molecular structures is used to generate start transformations, which are then iteratively improved to compute large common substructures. The results of the pairwise comparisons are efficiently merged using binary matching trees. All common substructures that were found, whether they are common to all or only a few molecules, are ranked according to different criteria, such as number of molecules containing the substructure, size of substructure, and geometric fit. For evaluating the geometric fit, we extend a known scoring function by introducing weights which allow to favor potential pharmacophore points. Despite considering the full atomic information for identifying multiple structural similarities, our algorithm is quite fast. Thus it is well suited as an interactive tool for the exploration of structural similarities of drug-sized molecules.
One crucial step in virtual drug design is the identification of new lead structures with respect to a pharmacological target molecule. The search for new lead structures is often done with the help of a pharmacophore, which carries the essential structural as well as physico-chemical properties that a molecule needs to have in order to bind to the target molecule. In the absence of the target molecule, such a pharmacophore can be established by comparison of a set of active compounds. In order to identify their common features,a multiple alignment of all or most of the active compounds is necessary. Moreover, since the “outer shape” of the molecules plays a major role in the interaction between drug and target, an alignment algorithm aiming at the identification of common binding properties needs to consider the molecule’s “outer shape”, which can be approximated by the solvent excluded surface. In this thesis, we present a new approach to molecular surface alignment based on a discrete representation of shape as well as physico-chemical properties by points distributed on the solvent excluded surface. We propose a new method to distribute points regularly on a surface w.r.t. a smoothly varying point density given on that surface. Since the point distribution algorithm is not restricted to molecular surfaces, it might also be of interest for other applications. For the computation of pairwise surface alignments, we extend an existing point matching scheme to surface points, and we develop an efficient data structure speeding up the computation by a factor of three. Moreover, we present an approach to compute multiple alignments from pairwise alignments, which is able to handle a large number of surface points. All algorithms are evaluated on two sets of molecules: eight thermolysin inhibitors and seven HIV-1 protease inhibitors. Finally, we compare the results obtained from surface alignment with the results obtained by applying an atom alignment approach.
An intuitive and sparse representation of the void space of porous materials supports the efficient analysis and visualization of interesting qualitative and quantitative parameters of such materials. We introduce definitions of the elements of this void space, here called pore space, based on its distance function, and present methods to extract these elements using the extremal structures of the distance function. The presented methods are implemented by an image processing pipeline that determines pore centers, pore paths and pore constrictions. These pore space elements build a graph that represents the topology of the pore space in a compact way. The representations we derive from μCT image data of realistic soil specimens enable the computation of many statistical parameters and, thus, provide a basis for further visual analysis and application-specific developments. We introduced parts of our pipeline in previous work. In this chapter, we present additional details and compare our results with the analytic computation of the pore space elements for a sphere packing in order to show the correctness of our graph computation.
We present iCon.text, a kiosk platform for the iPad centered around artefacts, whose content and layout can be tailored without programming skills for specific museum exhibitions. The central metaphor to access information is a virtual postcard with one front and a customizable number of back sides that provide details about exhibits to museum visitors in textual and image form. Back sides can link to others cards. Access to these postcards is possible through one or more navigation views that can be navigated to from a navigation bar.
The entry point to the application is designed as a multitouch interactive pile of cards in a playful manner that allows visitors of any age an easy approach to the presentation and interaction metaphor. To directly access a certain postcard, a mosaic view can be uitilized to provide an overview about all available exhibits. A category view groups postcards into themes. Locating artefacts on a zoomable map or exhibition floor plan allows for conveying information about spatial contexts between different objects and their location. Furthermore, contexts can be illustrated with a two stage view comprising an overview and corresponding detail views to provide further insights into the spatial, temporal, and thematic contexts of artefacts. The application scaffolding allows the design of bilingual presentations to support exhibitions with an international audience. The logo of the presenting institution or exhibition can be incorporated to display the the kiosk's corporate design branding and to access an imprint or further informations. Usage is logged into files to provide a basis for extracting statistical information about the usage.
The details about the exhibits are presented as images and as such impose no limit to the design choices made by the content provider or exhibition designer.
The application (enhanced with a panoramic view) has been integrated successfully into a large special exhibition about the ancient city of Pergamon 2011/2012 at the Pergamon Museum Berlin within the interdisciplinary project "Berlin Sculpture Network".
Kurzfassung. Durch die Alkalität des Betons wird Betonstahl dauerhaft vor
Korrosion geschützt. Infolge von Chlorideintrag kann dieser Schutz nicht länger
aufrechterhalten werden und führt zu Lochkorrosion. Die zerstörungsfreie Prüfung
von Stahlbetonproben mit 3D-CT bietet die Möglichkeit, eine Probe mehrfach
gezielt vorzuschädigen und den Korrosionsfortschritt zu untersuchen. Zur Quantifizierung
des Schädigungsgrades müssen die bei dieser Untersuchung anfallenden
großen Bilddaten mit Bildverarbeitungsmethoden ausgewertet werden. Ein wesentlicher
Schritt dabei ist die Segmentierung der Bilddaten, bei der zwischen Korrosionsprodukt
(Rost), Betonstahl (BSt), Beton, Rissen, Poren und Umgebung
unterschieden werden muss. Diese Segmentierung bildet die Grundlage für statistische
Untersuchungen des Schädigungsfortschritts. Hierbei sind die Änderung
der BSt-Geometrie, die Zunahme von Korrosionsprodukten und deren Veränderung
über die Zeit sowie ihrer räumlichen Verteilung in der Probe von Interesse. Aufgrund
der Größe der CT-Bilddaten ist eine manuelle Segmentierung nicht durchführbar,
so dass automatische Verfahren unabdingbar sind. Dabei ist insbesondere
die Segmentierung der Korrosionsprodukte in den Bilddaten ein schwieriges
Problem. Allein aufgrund der Grauwerte ist eine Zuordnung nahezu unmöglich,
denn die Grauwerte von Beton und Korrosionsprodukt unterscheiden sich kaum.
Eine formbasierte Suche ist nicht offensichtlich, da die Korrosionsprodukte in Beton
diffuse Formen haben.
Allerdings lässt sich Vorwissen über die Ausbreitung der Korrosionsprodukte
nutzen. Sie bilden sich in räumlicher Nähe des BSt (in Bereichen vorheriger
Volumenabnahme des BSt), entlang von Rissen sowie in Porenräumen, die direkt
am BSt und in dessen Nahbereich liegen. Davon ausgehend wird vor der
Korrosionsprodukterkennung zunächst eine BSt-Volumen-, Riss- und Porenerkennung
durchgeführt. Dieser in der Arbeit näher beschriebene Schritt erlaubt es, halbautomatisch
Startpunkte (Seed Points) für die Korrosionsprodukterkennung zu
finden. Weiterhin werden verschiedene in der Bildverarbeitung bekannte
Algorithmen auf ihre Eignung untersucht werden.
The most popular molecular surface in molecular visualization is the solvent excluded surface (SES). It provides information about the accessibility of a biomolecule for a solvent molecule that is geometrically approximated by a sphere. During a period of almost four decades, the SES has served for many purposes – including
visualization, analysis of molecular interactions and the study of cavities in molecular structures. However, if one is interested in the surface that is accessible to a molecule whose shape differs significantly from a sphere, a different concept is necessary. To address this problem, we generalize the definition of the SES by replacing the probe sphere with the full geometry of the ligand defined by the arrangement of its van der Waals spheres. We call the new surface ligand excluded surface (LES) and present an efficient, grid-based algorithm for its computation.
Furthermore, we show that this algorithm can also be used to compute molecular cavities that could host the ligand molecule. We provide a detailed description of its implementation on CPU and GPU. Furthermore, we present a performance and convergence analysis and compare the LES for several molecules, using as ligands either water or small organic molecules.
Tracing microtubule centerlines in serial section electron tomography requires microtubules to be stitched across sections, that is lines from different sections need to be aligned, endpoints need to be matched at section boundaries to establish a correspondence between neighboring sections, and corresponding lines need to be connected across multiple sections. We present computational methods for these tasks: 1) An initial alignment is computed using a distance compatibility graph. 2) A fine alignment is then computed with a probabilistic variant of the iterative closest points algorithm, which we extended to handle the orientation of lines by introducing a periodic random variable to the probabilistic formulation. 3) Endpoint correspondence is established by formulating a matching problem in terms of a Markov random field and computing the best matching with belief propagation. Belief propagation is not generally guaranteed to converge to a minimum. We show how convergence can be achieved, nonetheless, with minimal manual input. In addition to stitching microtubule centerlines, the correspondence is also applied to transform and merge the electron tomograms. We applied the proposed methods to samples from the mitotic spindle in C. elegans, the meiotic spindle in X. laevis, and sub-pellicular microtubule arrays in T. brucei. The methods were able to stitch microtubules across section boundaries in good agreement with experts’ opinions for the spindle samples. Results, however, were not satisfactory for the microtubule arrays. For certain experiments, such as an analysis of the spindle, the proposed methods can replace manual expert tracing and thus enable the analysis of microtubules over long distances with reasonable manual effort.
Structural properties of molecules are of primary concern in many fields. This report provides a comprehensive overview on techniques that have been developed in the fields of molecular graphics and visualization with a focus on applications in structural biology. The field heavily relies on computerized geometric and visual representations of three-dimensional, complex, large, and time-varying molecular structures. The report presents a taxonomy that demonstrates which areas of molecular visualization have already been extensively investigated and where the field is currently heading. It discusses visualizations for molecular structures, strategies for efficient display regarding image quality and frame rate, covers different aspects of level of detail, and reviews visualizations illustrating the dynamic aspects of molecular simulation data. The survey concludes with an outlook on promising and important research topics to foster further success in the development of tools that help to reveal molecular secrets.
Purpose/Aims of the Study: Bone’s hierarchical structure can be visualized using a variety of methods. Many techniques, such as light and electron microscopy generate two-dimensional (2D) images, while micro computed tomography (μCT) allows a direct representation of the three-dimensional (3D) structure. In addition, different methods provide complementary structural information, such as the arrangement of organic or inorganic compounds. The overall aim of the present study is to answer bone research questions by linking information of different 2D and 3D imaging techniques. A great challenge in combining different methods arises from the fact that they usually reflect different characteristics of the real structure.
Materials and Methods: We investigated bone during healing by means of μCT and a couple of 2D methods. Backscattered electron images were used to qualitatively evaluate the tissue’s calcium content and served as a position map for other experimental data. Nanoindentation and X-ray scattering experiments were performed to visualize mechanical and structural properties. Results: We present an approach for the registration of 2D data in a 3D μCT reference frame, where scanning electron microscopies serve as a methodic link. Backscattered electron images are perfectly suited for registration into μCT reference frames, since both show structures based on the same physical principles. We introduce specific registration tools that have been developed to perform the registration process in a semi-automatic way.
Conclusions: By applying this routine, we were able to exactly locate structural information (e.g. mineral particle properties) in the 3D bone volume. In bone healing studies this will help to better understand basic formation, remodeling and mineralization processes.